LEDs are usually powered with some nominal current, and dimmed by applying PWM to the current source output, rather than by continuously varying the current. In such a scenario, maximum brightness is achieved with 100% duty cycle, where no blinking happens at all, while minimum brightness can have a very low duty cycle, like 1%.
This means that a dimly-lit LED will light your hand only 1% of time. Suppose your hand is currently lit. This is the state when you see it first. Then after the lighting is turned off, some time passes while you can't see the hand move further. At the next PWM cycle the hand is lit again, and so on. This makes you see a "dashed" form of the motion blur. Another example would be if a fly or other insect flies by, you'll see it as if there's a train of flies, with the tail fading.